Find the roots of x^4 – 13x^2 + 36 = 0  

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The task is to:

Find the roots of x^4 – 13x^2 + 36 = 0

We can make the equation look friendlier by letting x^2=y.

Then the equation becomes:

y^2 - 13y + 36 = 0

Keeping in mind to obtain the number 13 from addition of factors of 36, and knowing that 36 can be obtained by multiplying 9 and 4, the factorization becomes:

(y-9)(y-4) = 0

Hence y=9 or 4.

That translate to x^2=9 => x=+3 or -3

or    x^2=4 =>  x=+2 or -2

(The entire section contains 2 answers and 220 words.)

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